Periodic solutions for prescribed mean curvature p-Laplacian equations with a singularity of repulsive type and a time-varying delay
Tóm tắt
In this article, the authors study the existence of positive periodic solutions for a prescribed mean curvature p-Laplacian equation with a singularity of repulsive type and a time-varying delay
$$\biggl(\varphi_{p} \biggl(\frac{x'(t)}{\sqrt{1+(x'(t))^{2}}} \biggr) \biggr)'+\beta x'(t)+g \bigl(t, x(t),x \bigl(t-\tau(t) \bigr) \bigr)=p(t), $$
where
$g\rightarrow-\infty$
when
$x\rightarrow0^{+}$
. The existence of positive periodic solutions conditions is devised by using the coincidence degree theory and some analysis methods. A numerical example demonstrates the validity of the main results.
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